Game theory provides useful insights into the way parties that share a scarce resource may plan their use of the resource under different situations. This review provides a brief and self-contained introduction to the theory of cooperative games. It can be used to get acquainted with the basics of cooperative games. Its goal is also to provide a basic introduction to this theory, in connection with a couple of surveys that analyze its use in the context of environmental problems and models. The main models (bargaining games, transfer utility, and non-transfer utility games) and issues and solutions are considered: bargaining solutions, single-value solutions like the Shapley value and the nucleolus, and multi-value solutions such as the core. The cooperative game theory (CGT) models that are reviewed in this paper favor solutions that include all possible players and ignore the strategic stages leading to coalition building. They focus on the possible results of the cooperation by answering questions such as: Which coalitions can be formed? And how can the coalitional gains be divided to secure a sustainable agreement? An important aspect associated with the solution concepts of CGT is the equitable and fair sharing of the cooperation gains.

Defence date: 23 March 2015; Examining Board: Professor Fernando Vega-Redondo, Supervisor, Bocconi University; Professor Piero Gottardi, EUI; Professor Paolo Pin, Università degli Studi di Siena; Professor Giovanni Ponti, Universidad de Alicante.; My thesis covers different aspects of applied game theory. The first paper looks at a two-sided asymmetric information game where agents make a collaborative decision not knowing each others' types. In the model, an intermediary has full knowledge about the types of agents and can make a decision that brings information to some types. However, once he puts the information on the table the agents are not obliged to pay him, which undermines his incentive to participate in the first place. I find that, nevertheless, the intermediary is still welfare-improving. In my second chapter I search for the optimal prize schemes in contests with sabotage. In the presence of sabotage, a standard prize scheme where all of the prize is given to the winner is no longer optimal as it creates very high incentives for sabotage. I show that in that case, an optimal prize structure may also assume a positive reward for contestants that are behind. With a higher number of contestants sabotage becomes a public good and therefore it is a lesser concern for the designer. In that case...

This research involves the design, development, and theoretical demonstration of models resulting in integrated misbehavior resolution protocols for ad hoc networked devices. Game theory was used to analyze strategic interaction among independent devices with conflicting interests. Packet forwarding at the routing layer of autonomous ad hoc networks was investigated. Unlike existing reputation based or payment schemes, this model is based on repeated interactions. To enforce cooperation, a community enforcement mechanism was used, whereby selfish nodes that drop packets were punished not only by the victim, but also by all nodes in the network. Then, a stochastic packet forwarding game strategy was introduced. Our solution relaxed the uniform traffic demand that was pervasive in other works. To address the concerns of imperfect private monitoring in resource aware ad hoc networks, a belief-free equilibrium scheme was developed that reduces the impact of noise in cooperation. This scheme also eliminated the need to infer the private history of other nodes. Moreover, it simplified the computation of an optimal strategy. The belief-free approach reduced the node overhead and was easily tractable. Hence it made the system operation feasible. Motivated by the versatile nature of evolutionary game theory...

In this work we have exposure to some elements of game theory and certain
resolution procedures games using matrices, probability and especially
optimization, ie, we optimize the moves with mathematical background.
For this we will use a Theorem, two Propositions and discuss several examples
to game theory, applying what we are working and show how one can
proceed in several games so that the reader can understand and use such a
theory.
The objective is to disseminate the ideas of game theory, which has
applications in several areas, including economy and military art.; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES; Neste trabalho teremos a exposição de alguns elementos da Teoria dos
Jogos e certos procedimentos de resolução de jogos usando matrizes, probabilidade
e principalmente otimização, ou seja, vamos otimizar as jogadas
com embasamento matemático. Para tal usaremos um Teorema, duas Proposi
ções e vários exemplos para discorrer sobre a Teoria dos Jogos, aplicando
o que estamos trabalhando e mostrar como se pode proceder em vários jogos
para que o leitor possa compreender e usar tal teoria.
O objetivo deste trabalho é divulgar as ideias da Teoria dos Jogos, as
quais tem aplicação em várias áreas...

The Traveler's Dilemma game and the Minimum Effort Coordination game are two social dilemmas that have attracted considerable attention due to the fact that the predictions of classical game theory are at odds with the results found when the games are studied experimentally. Moreover, a direct application of deterministic evolutionary game theory, as embodied in the replicator dynamics, to these games does not explain the observed behavior. In this work, we formulate natural variants of these two games as smoothed continuous-strategy games. We study the evolutionary dynamics of these continuous-strategy games, both analytically and through agent-based simulations, and show that the behavior predicted theoretically is in accord with that observed experimentally. Thus, these variants of the Traveler's Dilemma and the Minimum Effort Coordination games provide a simple resolution of the paradoxical behavior associated with the original games.

This paper is a survey of some of the ways in which the representation theory
of the symmetric group has been used in voting theory and game theory. In
particular, we use permutation representations that arise from the action of
the symmetric group on tabloids to describe, for example, a surprising
relationship between the Borda count and Kemeny rule in voting. We also explain
a powerful representation-theoretic approach to working with linear symmetric
solution concepts in cooperative game theory. Along the way, we discuss new
research questions that arise within and because of the
representation-theoretic framework we are using.; Comment: 20 pages

We study bargaining games between suppliers and manufacturers in a network
context. Agents wish to enter into contracts in order to generate surplus which
then must be divided among the participants. Potential contracts and their
surplus are represented by weighted edges in our bipartite network. Each agent
in the market is additionally limited by a capacity representing the number of
contracts which he or she may undertake. When all agents are limited to just
one contract each, prior research applied natural generalizations of the Nash
bargaining solution to the networked setting, defined the new solution concepts
of stable and balanced, and characterized the resulting bargaining outcomes. We
simplify and generalize these results to a setting in which participants in
only one side of the market are limited to one contract each. The heart of our
results uses a linear-programming formulation to establish a novel connection
between well-studied cooperative game theory concepts (such as core and
prekernel) and the solution concepts of stable and balanced defined for the
bargaining games. This immediately implies one can take advantage of the
results and algorithms in cooperative game theory to reproduce results such as
those of Azar et al. [1] and Kleinberg and Tardos [29] and also generalize them
to our setting. The cooperative-game-theoretic connection also inspires us to
refine our solution space using standard solution concepts from that literature
such as nucleolus and lexicographic kernel. The nucleolus is particularly
attractive as it is unique...

This book summarizes ongoing research introducing probability space
isomorphic mappings into the strategy spaces of game theory. This approach is
motivated by discrepancies between probability theory and game theory when
applied to the same strategic situation. In particular, probability theory and
game theory can disagree on calculated values of the Fisher information, the
log likelihood function, entropy gradients, the rank and Jacobian of variable
transforms, and even the dimensionality and volume of the underlying
probability parameter spaces. These differences arise as probability theory
employs structure preserving isomorphic mappings when constructing strategy
spaces to analyze games. In contrast, game theory uses weaker mappings which
change some of the properties of the underlying probability distributions
within the mixed strategy space. Here, we explore how using strong isomorphic
mappings to define game strategy spaces can alter rational outcomes in simple
games . Specific example games considered are the chain store paradox, the
trust game, the ultimatum game, the public goods game, the centipede game, and
the iterated prisoner's dilemma. In general, our approach provides rational
outcomes which are consistent with observed human play and might thereby
resolve some of the paradoxes of game theory.; Comment: 160 pages...

In this paper, we propose a bid optimizer for sponsored keyword search
auctions which leads to better retention of advertisers by yielding attractive
utilities to the advertisers without decreasing the revenue to the search
engine. The bid optimizer is positioned as a key value added tool the search
engine provides to the advertisers. The proposed bid optimizer algorithm
transforms the reported values of the advertisers for a keyword into a
correlated bid profile using many ideas from cooperative game theory. The
algorithm is based on a characteristic form game involving the search engine
and the advertisers. Ideas from Nash bargaining theory are used in formulating
the characteristic form game to provide for a fair share of surplus among the
players involved. The algorithm then computes the nucleolus of the
characteristic form game since we find that the nucleolus is an apt way of
allocating the gains of cooperation among the search engine and the
advertisers. The algorithm next transforms the nucleolus into a correlated bid
profile using a linear programming formulation. This bid profile is input to a
standard generalized second price mechanism (GSP) for determining the
allocation of sponsored slots and the prices to be be paid by the winners. The
correlated bid profile that we determine is a locally envy-free equilibrium and
also a correlated equilibrium of the underlying game. Through detailed
simulation experiments...

Classical game theory treats players as special---a description of a game
contains a full, explicit enumeration of all players---even though in the real
world, "players" are no more fundamentally special than rocks or clouds. It
isn't trivial to find a decision-theoretic foundation for game theory in which
an agent's coplayers are a non-distinguished part of the agent's environment.
Attempts to model both players and the environment as Turing machines, for
example, fail for standard diagonalization reasons.
In this paper, we introduce a "reflective" type of oracle, which is able to
answer questions about the outputs of oracle machines with access to the same
oracle. These oracles avoid diagonalization by answering some queries randomly.
We show that machines with access to a reflective oracle can be used to define
rational agents using causal decision theory. These agents model their
environment as a probabilistic oracle machine, which may contain other agents
as a non-distinguished part.
We show that if such agents interact, they will play a Nash equilibrium, with
the randomization in mixed strategies coming from the randomization in the
oracle's answers. This can be seen as providing a foundation for classical game
theory in which players aren't special.; Comment: Extended version of "Reflective Oracles: A Foundation for Game Theory
in Artificial Intelligence" accepted to LORI-V

Game theoretical techniques have recently become prevalent in many
engineering applications, notably in communications. With the emergence of
cooperation as a new communication paradigm, and the need for self-organizing,
decentralized, and autonomic networks, it has become imperative to seek
suitable game theoretical tools that allow to analyze and study the behavior
and interactions of the nodes in future communication networks. In this
context, this tutorial introduces the concepts of cooperative game theory,
namely coalitional games, and their potential applications in communication and
wireless networks. For this purpose, we classify coalitional games into three
categories: Canonical coalitional games, coalition formation games, and
coalitional graph games. This new classification represents an
application-oriented approach for understanding and analyzing coalitional
games. For each class of coalitional games, we present the fundamental
components, introduce the key properties, mathematical techniques, and solution
concepts, and describe the methodologies for applying these games in several
applications drawn from the state-of-the-art research in communications. In a
nutshell, this article constitutes a unified treatment of coalitional game
theory tailored to the demands of communications and network engineers.; Comment: IEEE Signal Processing Magazine...

This paper presents a monoidal category whose morphisms are games (in the
sense of game theory, not game semantics) and an associated diagrammatic
language. The two basic operations of a monoidal category, namely categorical
composition and tensor product, correspond roughly to sequential and
simultaneous composition of games. This leads to a compositional theory in
which we can reason about properties of games in terms of corresponding
properties of the component parts. In particular, we give a definition of Nash
equilibrium which is recursive on the causal structure of the game.
The key technical idea in this paper is the use of continuation passing style
for reasoning about the future consequences of players' choices, closely based
on applications of selection functions in game theory. Additionally, the clean
categorical foundation gives many opportunities for generalisation, for example
to learning agents.

Here we present a ground-breaking new postulate for game theory. The first
part of this postulate contains the axiomatic observation that all games are
created by a designer, whether they are: e.g., (dynamic/static) or
(stationary/non-stationary) or (sequential/one-shot) non-cooperative games, and
importantly, whether or not they are intended to represent a non-cooperative
Stackelberg game, they can be mapped to a Stackelberg game. I.e., the game
designer is the leader who is totally rational and honest, and the followers
are mapped to the players of the designed game. If now the game designer, or
"the leader" in the Stackelberg context, adopts a pure strategy, we postulate
the following second part following from axiomatic observation of ultimate game
leadership, where empirical insight leads to the second part of this postulate.
Importantly, implementing a non-cooperative Stackelberg game, with a very
honest and rational leader results in social optimality for all players
(followers), assuming pure strategy across all followers and leader, and that
the leader is totally rational, honest, and is able to achieve a minimum amount
of competency in leading this game, with any finite number of iterations of
leading this finite game.; Comment: 3 pages